We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

ePUZSOLVED is designed to help students understand the general communication models and experience the advantages and disadvantages of each. It will highlight how various modes of communication, when used appropriately, may lead people to solve problems, as exemplified by the online puzzle. Courses: Introduction of Communication Models, Review of…

Nuclear magnetic resonance (NMR) spectroscopy is a very powerful analytical method that has found many applications in physics, chemistry, biology, and medicine. It is an indispensable tool particularly for synthetic chemists because it can be used for a rapid elucidation of the structures of organic compounds. For this reason, NMR spectral…

A digital escape room is a gamified activity in which students work collaboratively to solve a series of tasks or riddles within a certain amount of time. They are typically embedded in a story framework at the end of which students need to "escape" an imaginary scenario. Students explore the target culture while using the target…

The overarching goal of this review article is to discuss and provide evidence of ways that visual displays can be used to improve classroom thinking skills. Specifically, we attempt to first, provide a synthesis of the relationship among visual displays, visual literacy, and visual thinking. Second, we review the relatively scant educational…

Geometrography, "alias the art of geometric constructions" was proposed by Emile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions, capable of: designate every geometric construction by a pair of values that manifests its…

This paper presents a model for mastery learning. The framework for this model overlays the cognitive and knowledge dimensions from Krathwohl's revision of Bloom's Taxonomy, the Revised Taxonomy, with Polanyi's theory of personal knowledge. A simplified framework integrates Polanyi's concepts of subsidiary and focal awareness with the Revised…

A bachelor's degree program in chemistry typically starts with basic concepts in mathematics, physics, and chemistry. Those principles are very important because they pave the ground for future advanced studies and, therefore, one needs to present them in a clear but rigorous way. One example is provided by the mathematical notion of an iterative…

To fulfill the Standards for Mathematical Practice (National Governors Association Center for Best Practices & Council of Chief State School Officers [NGA Center & CCSSO], 2010), it is important for teachers to empower students to critique, revise, and expand their ideas as they solve problems. However, students often face challenges such…

Collaborative Problem Solving (CPS) skills are receiving increased attention in the current workforce and in lifelong learning. In learning and labor contexts, successful teamwork is however not always guaranteed, due to several reasons, such as an unequal level of individual participation. Training in CPS for all groups is therefore needed.…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

Too often, high school algebra students encounter topics in a discrete, disconnected fashion. In the authors' first years of teaching, they found students to be adept at solving problems they were currently studying; for instance, they could solve quadratics during a quadratics unit. Too often, however, students struggled with that same content…

Understanding the concepts of quantum mechanics has always been a challenge for undergraduate students. This is especially so because many of the introductory (analytically solvable) systems and problems discussed in textbooks are seemingly abstract. Using approximate experimental demonstrations of such systems and problems have been shown to be…

This work presents a discussion about the Didactic Training Engineering (EDF) methodology, of French origin, emphasizing the role of the teacher, during his initial or continuous training, through the conception and structuring of a didactic situation, organized by such methodology and based on the Theory of Didactic Situations (TSD). Therefore,…

Understanding spatial reasoning is important to success in mathematics. This article shows how the proficiency strands in the "Australian Curriculum: Mathematics" provide the tools needed for effective teaching and learning of spatial thinking.